SELF-CALIBRATING NOx SENSOR

ABSTRACT

A system for calibrating a response to an exhaust-stream NO x  level in a motor vehicle is provided. The system comprises a NO x  sensor that includes an electrode, a current from the electrode responsive to the exhaust-stream NO x  level while a bias voltage is applied to the electrode. The system further comprises a controller configured to interrupt the bias voltage and to adjust a motor-vehicle response to the current based at least partly on an attained voltage of the electrode while the bias voltage is interrupted. Other embodiments provide a method of calibrating a NO x  sensor response in terms of gain and offset parameters.

TECHNICAL FIELD

The present application relates to emissions control in motor vehicles,and more particularly, to nitrogen oxide (NO_(x)) emissions from motorvehicles.

BACKGROUND AND SUMMARY

Various emissions from motor-vehicle exhaust systems are regulated, suchas NO_(x) emission. To limit NO_(x) emission while maintainingperformance, a motor-vehicle may be configured, in a closed-loop manner,to tighten emission control when an exhaust-stream NO_(x) levelincreases. Tightening control may include, for example, supplying aricher air/fuel mixture to a combustion chamber of the motor vehicle orenabling reductive regeneration of an exhaust-stream NO_(x) trap.

For some control systems to function effectively, an accurate estimateof the NO_(x) level may be generated from a NO_(x) sensor. U.S. Pat. No.4,770,760 describes a NO_(x) sensor comprising two electrochemical pumpcells in series, with a diffusion restrictor upstream of each pump cell.In the cited reference, the NO_(x) level in an analyte is indicated by adiffusion-limited current flowing to a catalyzed electrode in adownstream pump cell, an upstream pump cell being used to reduce thepartial pressure of oxygen (O₂) to a fixed, low level, so that theNO_(x) level can be estimated with a minimum of interference.

In the decade since this technology was developed, numerous attemptshave been made to improve the accuracy, reliability, and longevity ofelectrochemical NO_(x) sensors. For example, U.S. Pat. No. 6,059,947describes a NO_(x) sensor providing feedback control of a set-pointvoltage in the upstream pump cell, and a self-diagnosis feature coupledto the feedback control. The feedback control adjusts the set-pointvoltage so that the partial pressure of O₂ in the second pump cellremains constant despite aging of sensor components and changes inanalyte O₂ level. The self-diagnosis feature compares the adjusted setpoint against predetermined limits to assess sensor degradation.

However, the above reference fails to address other ageing effectscommonly observed in electrochemical NO_(x)-sensor response: namely, agradual reduction in gain and an increase in offset in the correlationbetween the sensed parameters and NO_(x) in the exhaust stream. Thesefactors, which contribute to uncertainty in the detected NO_(x) level,may be caused by degradation losses occurring on prolonged operation ofthe NO_(x) sensor: losses in electrolyte conductance, for example, or inelectroactivity and/or electroactive surface area of one or moreelectrodes.

The inventors herein have recognized the above problems and have deviseda series of approaches to address them. Thus, in one embodiment, asystem for calibrating a response to an exhaust-stream NO_(x) level in amotor vehicle is provided. The system comprises a NO_(x) sensor thatincludes an electrode, a current from the electrode responsive to theexhaust-stream NO_(x) level while a bias voltage is applied to theelectrode. The system further comprises a controller configured tointerrupt the bias voltage and to adjust a motor-vehicle response to thecurrent based at least partly on an attained voltage of the electrodewhile the bias voltage is interrupted.

By calibrating the motor-vehicle response based on the attained voltage,the motor-vehicle response may track the exhaust-stream NO_(x) levelwith greater fidelity despite degradation losses in the NO_(x) sensor,such as those indicated above.

Other embodiments disclosed herein provide a method of calibrating aresponse to an exhaust-stream NO_(x) level in a motor vehicle. Stillother embodiments provide a method of calibrating the NO_(x) sensorresponse in terms of gain and offset parameters.

It should be understood that the summary above is provided to introducein simplified form a selection of concepts that are further described inthe detailed description. It is not meant to identify key or essentialfeatures of the claimed subject matter, the scope of which is defineduniquely by the claims that follow the detailed description.Furthermore, the claimed subject matter is not limited toimplementations that solve any disadvantages noted above or in any partof this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a NO_(x) sensor with associated control and measurementelectronics in accordance with the present disclosure. The drawing isschematic and renders the NO_(x) sensor in cross section.

FIG. 2 is a flow chart illustrating an example NO_(x)-sensorself-calibration procedure in accordance with the present disclosure.

FIG. 3 is a flow chart illustrating an emissions-control procedure,which includes a NO_(x)-sensor self-calibration procedure, in accordancewith the present disclosure.

DETAILED DESCRIPTION

FIG. 1 shows a schematic, cross-sectional view of an example NO_(x)sensor. In particular, FIG. 1 shows NO_(x) sensor 102 comprising firstlayer 104, second layer 106, third layer 108, fourth layer 110, fifthlayer 112, and sixth layer 114. At least the first and third layerscomprise an oxide (O²⁻) conducting solid electrolyte material, e.g., azirconia (ZrO₂) containing ceramic. The remaining layers may comprisethe same and/or different materials: other ceramics, for example,selected to bond reliably to the first and third layers, to have similarcoefficients of thermal expansion, etc.

NO_(x) sensor 102 further includes upstream cavity 116, downstreamcavity 118, reference cavity 120, first diffusion restrictor 122, andsecond diffusion restrictor 124. Each of the upstream, downstream, andreference cavities is a void space formed in the layered structure ofthe NO_(x) sensor and configured to confine a specimen of gas. Inparticular, upstream cavity 116 and downstream cavity 118 are configuredto confine analyte-derived gas, and reference cavity 120 is configuredto confine air. It will be understood that ‘confine,’ as used in thiscontext, need not imply long-term confinement. In the illustratedembodiment, air may enter the reference cavity from the right sideexterior the sensor.

First diffusion restrictor 122 is a material zone that restricts adiffusion of analyte gas into the upstream cavity. In the illustratedembodiment, analyte gas, which may include gas from a motor-vehicleexhaust stream, may penetrate the first diffusion restrictor from theleft side exterior the sensor. First diffusion restrictor 122 mayinclude one or more small apertures through which analyte gas maycommunicate with the upstream cavity; it may be a porous materialincluding but not limited to a porous ZrO₂-containing ceramic. Seconddiffusion restrictor 124 is a material zone that restricts a diffusionof gas from the upstream cavity to the downstream cavity. The seconddiffusion restrictor may be substantially the same or at least partlydifferent than the first diffusion restrictor.

NO_(x) sensor 102 further includes insulator 126 and resistive heater128. Insulator 126 is an electrically insulating and ionicallyinsulating material, e.g., a ceramic such as alumina, selected to bondreliably to the first and third layers, to have similar coefficients ofthermal expansion, etc. Insulator 126 may include a groove into whichresistive heater 128 is entrained. Resistive heater 128 is a resistive,electrical conductor configured to support a flow of current and therebyto supply heat to NO_(x) sensor 102.

NO_(x) sensor 102 further includes upstream cathode 130, upstream anode132, and reference electrode 134. Each of the upstream cathode, theupstream anode, and the reference electrode may be a porous cermet-typeelectrode. Each may include a corrosion-resistant, refractory metal suchas a platinum-group metal and a ceramic selected to bond reliably to thefirst and third layers, to have similar coefficients of thermalexpansion, etc. In a manner well-known in the art, a formulation ofupstream cathode 130 may be selected for its lack of catalytic activitytoward NO_(x).

NO_(x) sensor 102 further includes downstream cathode 136 andNO_(x)-sensing electrode 138. Each of the downstream cathode and theNO_(x)-sensing electrode may be substantially the same or at leastpartly different than the electrodes described above. However, aformulation of NO_(x)-sensing electrode 138 may be selected, in a mannerwell-known in the art, especially for its significant catalytic activitytoward NO_(x).

FIG. 1 shows example control and measurement electronics operativelycoupled to NO_(x) sensor 102. In FIG. 1, some of the control andmeasurement electronics are shown in schematic detail; the rest arereferred to collectively as NO_(x)-sensor controller 140. It must beunderstood, however, that this distinction is for illustrative purposesonly, as any control or measurement component described herein may beintegrated into, or located outside of, any motor-vehicle controldevice.

FIG. 1 shows current source 142, which draws current I₀ from upstreamcathode 130 and supplies the same current to upstream anode 132. Notethat the direction of current flow, by convention, is opposite the flowof electrons and other negative charge carriers. Thus, the current I₀ issuch as to reduce molecular oxygen (02) at upstream cathode 130, tocarry the O²⁻ so formed through first layer 104, and to oxidize the O²⁻back to O₂ at upstream anode 132. Upstream cathode 130, upstream anode132, and intervening first layer 104 are therefore configured to pump O₂out of upstream cavity 116. Collectively, the upstream cathode, theupstream anode, and the first layer are referred to as the upstream pumpcell.

By pumping 02 out of upstream cavity 116 faster than it can enterthrough diffusion restrictor 122, the upstream pump cell may reduce thepartial pressure of O₂ in the upstream cavity relative to that of theanalyte. As an approximation, and subject to conditions and assumptionswell-known in the art, the partial pressure of O₂ in the upstream cavityis given by a Nernst relation:

V ₀ =R T ln(s ₁₃₀ /s ₁₃₄)/2F=R T ln(p ₁₁₆ /p ₁₂₀)/2F.   (1)

In eq 1, V₀ is a voltage measured between upstream cathode 130 andreference electrode 134, R is the gas constant, T is the absolutetemperature, F is Faraday's constant, s₁₃₀ is the concentration of O₂sorbed on upstream cathode 130, s₁₄₃ is the concentration of O₂ sorbedon reference electrode 134, p₁₁₆ is the partial pressure of O₂ inupstream cavity 116, and p₁₂₀ is the partial pressure of O₂ in referencecavity 120. The right-hand side of eq 1 recognizes that a rapidequilibrium exchanges sorbed and gas-phase O₂ in the upstream cavity.Thus, NO_(x)-sensor controller 140 may be configured to dynamicallyadjust the value of I₀ to maintain a constant value of V₀, which maycorrespond to a constant, low value of p₁₁₆. In that way, the partialpressure of O₂ in upstream cavity 116 may be maintained at a constant,low value.

FIG. 1 shows first voltage source 144, which provides bias voltage B₁between downstream cathode 136 and reference electrode 134. Themagnitude of bias voltage B₁ may be such that reduction of O₂ at thedownstream cathode is diffusion-limited. Thus, O₂ is reduced just asfast as it can diffuse to the downstream cathode, which is the rate atwhich it penetrates second diffusion restrictor 124. Therefore, thepartial pressure of O₂ in downstream cavity 118 is maintained at aconstant level, lower than the level in upstream cavity 116. Downstreamcathode 136, reference electrode 134, and intervening third layer 108are configured to pump O₂ out of downstream cavity 118; collectively,these components are referred to as the downstream pump cell.

FIG. 1 shows switch 146 and second voltage source 148. When switch 146is closed, second voltage source 148 provides bias voltage B₂ betweenNO_(x)-sensing electrode 138 and reference electrode 134. NO_(x)-sensorcontroller 140 may be configured to close switch 146 to provide orrestore bias voltage B₂ and to open switch 146 to interrupt bias voltageB₂. Thus, switch 146 may be any electrically controllable switch,whether electromechanical or semiconductor-based.

The magnitude of bias voltage B₂ may be such that reduction of O₂ atNO_(x)-sensing electrode 138 is diffusion-limited. However, the flux ofO₂ to the NO_(x)-sensing electrode may be quite small because of thesmall size of this electrode relative to downstream cathode 136 andbecause it is located farther from second diffusion restrictor 124. Inthe illustrated embodiment, O₂-reduction current observed at theNO_(x)-sensing electrode corresponds to an interference, i.e., anoffset, in the current-based NO_(x) estimate to be described presently.Reduction of other chemical species, e.g. water, may further contributeto the offset.

As indicated above, NO_(x)-sensing electrode 138 differs from downstreamcathode 136 not only in size and location, but also in catalyst loading.In particular, the NO_(x)-sensing electrode is configured to besignificantly catalytic toward NO_(x) while the downstream cathode isconfigured to be minimally catalytic toward NO_(x). Thus, the chemicalconstituents of NO_(x) may be electrochemically reduced at theNO_(x)-sensing electrode, e.g.,

NO₂+2e⁻→NO+O²⁻, and   (2)

2NO+4e⁻→N₂+2O²⁻.   (3)

In addition, the chemical constituents of NO_(x) may be decomposed atthe NO_(x)-sensing electrode, e.g.,

2NO₂→2NO+O₂, and   (4)

2NO→N₂+O₂,   (5)

to yield sorbed O₂, which in turn may be reduced at the NO_(x)-sensingelectrode. Whether by catalyzed electrochemical reduction, by catalyzeddecomposition followed by electrochemical reduction, or by somecombination of these, the current I₂ may therefore reflect a level ofNO_(x) in the analyte over and above the offset. For example,

I ₂ =G p+H,   (6)

where p is a partial pressure of a NO_(x) constituent: nitric oxide(NO), nitrogen dioxide (NO₂), dinitrogen tetraoxide (N₂O₄), or nitrousoxide (N₂ 0), as examples; G is the sensor gain with respect to thatconstituent, and H is the sensor offset. In examples where the analyteis derived from motor-vehicle exhaust and may include different NO_(x)constituents simultaneously, a composite sensor gain may be definedbased on predicted proportions of the various NO_(x) constituents in theexhaust.

On prolonged use, however, the gain and offset of the NO_(x) sensor mayboth change. Changes in these parameters may result from an ageing ofvarious sensor components: electrodes, diffusion restrictors, andelectrolyte layers, for example. To compensate for changing sensor gainand sensor offset, NO_(x)-sensor controller 140 may be furtherconfigured to enable self-calibration of NO_(x) sensor 102.

Thus, when switch 146 is open, bias voltage B₂ to NO_(x)-sensingelectrode 138 is interrupted. Under such conditions, the voltagemeasured between the NO_(x)-sensing electrode and the referenceelectrode is given by another Nernst relation. As an approximation, andsubject to conditions and assumptions well-known in the art,

V ₂ =R T ln(s ₁₃₈ /s ₁₃₄)/2F.   (7)

In eq 6, s₁₃₈ refers to the concentration of O₂ sorbed on NO_(x)-sensingelectrode 138. Due to the catalyst loading of NO_(x)-sensing electrode138, s₁₃₈ may not be related in a straightforward way to the partialpressure of O₂ in the cavity in which the electrode is disposed-incontrast to eq 1. This is because NO_(x) decomposition (eqs 4 and 5, forexample) supplies additional O₂ to the surface of NO_(x)-sensingelectrode 138 at a rate that may exceed the rate of exchange of sorbedand gas-phase O₂. Thus, s₁₃₈ may increase with increasing NO_(x) levelin the analyte.

An open-circuit or near open-circuit V₂ measurement may thereforeprovide an independent, calibrating estimate of the NO_(x) level,against which the I₂-based estimate may be compared. In one example, aperiodically acquired V₂-based estimate of the NO_(x) level may be usedto refine gain and offset parameters used in the I₂-based estimate.

To enable self calibration, NO_(x)-sensor controller 140 may includeanalog electronics comprising operational amplifiers, for example,and/or digital electronics comprising a memory, a microprocessor, alook-up table, and/or other components known in the art to enablefixed-function calculation, parameter storage, and/or adjustable-gainamplification. NO_(x)-sensor controller 140 may further includeappropriate timing componentry to enable collection of multiple voltagesamples according to a schedule.

The example configuration illustrated in FIG. 1 may be used as part ofan emissions-control system of a motor vehicle. FIG. 1 illustrates, inone specific example, a NO_(x)-sensor including an electrode, where acurrent from the electrode may be responsive to an exhaust-stream NO_(x)level in a motor vehicle while a bias voltage is applied to theelectrode. In many instances, the motor vehicle in which the NO_(x)sensor is installed may be configured to respond in some way to thecurrent. For example, the motor-vehicle response to the current mayinclude reducing a NO_(x) emission in response to the current. Reducingthe NO_(x) emission may take several different forms depending on theparticular motor-vehicle configuration. In some embodiments, the motorvehicle response to the current may include regenerating anexhaust-aftertreatment device in response to the current. In otherexamples, the motor-vehicle response to the current may include reducingan air-to-fuel ratio in a combustion chamber in response to the current.

In each of these embodiments, a controller may be further configured toadjust the motor-vehicle response to the current based at least partlyon an attained voltage of the electrode during a period in which thebias voltage is interrupted (V₂ in the illustrated embodiment). In oneexample, the controller may do so by refining the NO_(x)-sensor gain andoffset parameters used in an emission-control operation, based on theattained voltage. This is an example of NO_(x)-sensor self-calibration,details of which are described below, with reference to FIGS. 2 and 3.FIG. 2 illustrates an example NO_(x)-sensor self-calibration procedure,while FIG. 3 illustrates a manner in which NO_(x)-sensor selfcalibration may be incorporated into an emissions-control strategy of amotor vehicle.

FIG. 2 is a flow chart illustrating example NO_(x)-sensorself-calibration procedure 200. Procedure 200 is one example of a methodof calibrating a response to an exhaust-stream NO_(x) level in a motorvehicle, where the motor vehicle includes a NO_(x) sensor. The methodincludes interrupting a bias voltage to an electrode of the NO_(x)sensor, a current from the electrode responsive to the exhaust-streamNO_(x) level absent said interrupting. The method further includesadjusting a motor-vehicle response to the current based at least partlyon an attained voltage of the electrode during said interrupting. Moreparticularly, procedure 200 includes adjusting a gain and an offset ofthe NO_(x) sensor based at least partly on an attained voltage of theelectrode during said interrupting.

In describing procedure 200, continued reference is made to thecomponents of FIG. 1. The procedure may be executed by anemissions-control system of a motor vehicle in a manner illustrated inFIG. 3.

At 202, NO_(x)-sensor controller 140 interrupts bias voltage B₂ toNO_(x)-sensing electrode 138. The NO_(x) sensor controller may interruptthe bias by opening switch 146, for example. When bias voltage B₂ isinterrupted, current I₂ ceases to reflect the NO_(x) level in theanalyte. At 204, NO_(x)-sensor controller 140 schedules a sampling ofvoltage V₂ over a predetermined period of time. In one non-limiting andpurely illustrative example, NO_(x)-sensor controller 140 may schedulefifty V₂ samples to be recorded at open-circuit, over a period of 25seconds, at evenly-spaced, 500-millisecond intervals. Details of thescheduling may differ from one motor-vehicle system to the next, and mayalso depend on operating conditions. For example, when a previous I₂measurement has indicated that the exhaust-stream NO_(x) level isrelatively high, the sampling period may be relatively short. Incontrast, when a previous I₂ measurement has indicated that the NO_(x)level is relatively low, the sampling period may be relatively long.Thus the duration of bias voltage interruption and voltage sampling maybe responsive to I₂. A greater sampling period may be advantageous whenthe NO_(x) level is low because more time may be needed for sorbed,active species on NO_(x)-sensing electrode 138 to come to equilibriumwith gas-phase NO_(x) in downstream cavity 118.

At 206, NO_(x)-sensor controller 140 determines whether it is time torecord a V₂ sample. If it is not time to record a V₂ sample, thenexecution of procedure 200 pauses, at 208, for a predetermined period oftime. It should be understood that ‘pause,’ used herein, implies onlythat the illustrated procedure is paused. Execution of other relatedand/or unrelated control routines may continue, and in some embodiments,step 208 may include a programmed interrupt to other such controlroutines. After the pause, execution resumes at 206, where theNO_(x)-sensor controller again determines if it is time to sample V₂. Ifit is time to sample V₂, then at 210, the NO_(x)-sensor controllersamples V₂. V₂ may be sampled at or near open-circuit to avoidconcentration polarization in layer 108 at an interface withNO_(x)-sensing electrode 138.

After V₂ is sampled, the NO_(x)-sensor controller determines, at 212,whether V₂-sampling is completed or whether further sampling isrequired. The NO_(x)-sensor controller may make the determination basedon the time, a number of samples recorded, etc. If V₂-sampling is notcompleted, then execution resumes at 206; if V₂-sampling is completed,then execution continues to 214, where the recorded V₂ array isprocessed. In one example, processing the V₂ array may include fittingV₂-versus-time data to a predicted mathematical model, i.e., a curve,such as an exponential decay. From the fitted model parameters, it maybe possible to estimate a steady-state value of V₂ at the analyte NO_(x)level, even if V₂ sampling is stopped before the steady-state isreached. Thus, the NO_(x)-sensor controller may be configured toextrapolate to a steady-state value of V₂. In other embodiments, theNO_(x)-sensor controller may be configured to discard V₂ samples in aperiod over which V₂ is trending rapidly, and to average V₂ samples in aperiod over which V₂ is substantially constant, is deviating randomly,and/or is trending slowly.

Processing the V₂ array may further include relating the steady-state oraverage V₂, as obtained above, to a predicted, analyte NO_(x) level. Thepredicted NO_(x) level may be obtained from V₂ by using a calculationexecuted by NO_(x)-sensor controller 140, a look-up table, etc.

At 216, the NO_(x) level so obtained is compared to a NO_(x) levelpreviously obtained from an I₂-based estimate, and a gain or offsetparameter used in the I₂-based estimate is adjusted so that the twoNO_(x)-level estimates coincide.

To adjust both gain and offset parameters, calibration at two or moredifferent NO_(x) levels is necessary. Thus, NO_(x)-sensor controller 140may be configured to initially adjust the gain parameter only, whileholding the offset parameter fixed, and then to adjust the offsetparameter when data from a range of different NO_(x) levels becomesavailable. In some embodiments, adjustment of gain and offset may beexecuted iteratively, holding one fixed while the other is adjusted. Inother embodiments, data representing multiple NO_(x) levels may be heldin memory and fit globally to a two-parameter model. By these andsimilar methods, NO_(x) sensor 102 may be self calibrated.

At 218, NO_(x)-sensor controller 140 restores bias voltage B₂ toNO_(x)-sensing electrode 138. The NO_(x) sensor controller may restorethe bias by closing switch 146, for example. When bias voltage B₂ isrestored, current I₂ may again reflect the NO_(x) level in the analyte.

FIG. 3 is a flow chart illustrating example emissions-control procedure300, which includes NO_(x)-sensor self-calibration procedure 200. Indescribing the procedure, continued reference is made to the componentsof FIG. 1. Procedure 300 may be executed by an emissions-control systemof a motor vehicle.

At 302, the emissions-control system updates a NO_(x)-sensorself-calibration schedule. In one embodiment, the self-calibrationschedule may be based on a fixed time interval, e.g., self calibrateonce a day. In other embodiments, the self-calibration schedule may beresponsive to an age of the NO_(x) sensor, a motor-vehicle run time, oron a number of miles accumulated. In some embodiments, theself-calibration schedule may be responsive to some other property ofthe NO_(x) sensor that is interrogated by the controller: I₀ or I₁, forexample, where values outside of a predetermined range may point tosensor degradation. In some embodiments, it may be advantageous thatself-calibration be delayed for a period of time following a cold startof the motor vehicle, and/or for a different period of time following anexhaust-aftertreatment device regeneration in the motor vehicle. Thecontroller may therefore be configured to delay interrupting biasvoltage V₂ for such periods of time. In some examples, theself-calibration schedule may be adjusted based on the NO_(x) level asreflected by I₂. For example, the periods of delay indicated above maybe responsive to I₂.

At 304, the emissions-control system determines whether it is time forNO_(x)-sensor self calibration. If it is not time for NO_(x)-sensor selfcalibration, then at 306, procedure 300 is paused. Execution of otherrelated and/or unrelated control routines may continue, and in someembodiments, step 306 may include a programmed interrupt to other suchcontrol routines. After the pause, execution resumes at 302, where theemissions-control system again updates the NO_(x)-sensorself-calibration schedule, which may depend on changing conditions.

Returning now to step 304, if it is time for NO_(x)-sensor selfcalibration, then at 200, self-calibration is executed as illustrated byexample in FIG. 2. After self-calibration is completed, executionresumes again at step 302.

Note that the example control and estimation routines included hereincan be used with various system configurations. The specific routinesdescribed herein may represent one or more of any number of processingstrategies such as event-driven, interrupt-driven, multi-tasking,multi-threading, and the like. As such, various actions, operations, orfunctions illustrated may be performed in the sequence illustrated, inparallel, or in some cases omitted. Likewise, the order of processing isnot necessarily required to achieve the features and advantages of theexample embodiments described herein, but is provided for ease ofillustration and description. One or more of the illustrated actions,functions, or operations may be repeatedly performed depending on theparticular strategy being used. Further, the described operations,functions, and/or acts may graphically represent code to be programmedinto computer readable storage medium in the control system.

Further still, it should be understood that the systems and methodsdescribed herein are exemplary in nature, and that these specificembodiments or examples are not to be considered in a limiting sense,because numerous variations are contemplated. Accordingly, the presentdisclosure includes all novel and non-obvious combinations andsub-combinations of the various systems and methods disclosed herein, aswell as any and all equivalents thereof.

1. A system for calibrating a response to an exhaust-stream NO_(x) levelin a motor vehicle, the system comprising: a NO_(x) sensor including anelectrode, a current from the electrode responsive to the exhaust-streamNO_(x) level while a bias voltage is applied to the electrode; and acontroller configured to interrupt the bias voltage and to adjust amotor-vehicle response to the current based at least partly on anattained voltage of the electrode while the bias voltage is interrupted.2. The system of claim 1, further comprising a switch, wherein thecontroller is further configured to interrupt the bias voltage byopening the switch and to restore the bias voltage by closing theswitch.
 3. The system of claim 1, wherein the controller is furtherconfigured to delay interrupting the bias voltage for a period followinga cold start of the motor vehicle.
 4. The system of claim 3, wherein theperiod is responsive to the current.
 5. The system of claim 1, whereinthe controller is further configured to delay interrupting the biasvoltage for a period following an exhaust-aftertreatment deviceregeneration in the motor vehicle.
 6. The system of claim 1, wherein thecontroller is further configured to interrupt the bias voltagerepeatedly, according to a schedule.
 7. The system of claim 6, whereinthe schedule is responsive to an age of the NO_(x) sensor.
 8. The systemof claim 6, wherein the schedule is responsive to a property of theNO_(x) sensor interrogated by the controller.
 9. A method of calibratinga response to an exhaust-stream NO_(x) level in a motor vehicle, themotor vehicle including a NO_(x) sensor, the method comprising:interrupting a bias voltage to an electrode of the NO_(x) sensor, acurrent from the electrode responsive to the exhaust-stream NO_(x) levelabsent said interrupting; and adjusting a motor-vehicle response to thecurrent based at least partly on an attained voltage of the electrodeduring said interrupting.
 10. The method of claim 9, wherein themotor-vehicle response to the current includes reducing a NO_(x)emission in response to the current.
 11. The method of claim 9, whereinthe motor-vehicle response to the current includes regenerating anexhaust-aftertreatment device in response to the current.
 12. The methodof claim 9, wherein the motor-vehicle response to the current includesreducing an air-to-fuel ratio in a combustion chamber in response to thecurrent.
 13. The method of claim 9, wherein a duration of saidinterrupting is responsive to the current.
 14. The method of claim 13,wherein the duration increases as the current decreases.
 15. The methodof claim 9, further comprising sampling the attained voltage of theelectrode repeatedly while the current is interrupted.
 16. The method ofclaim 15, further comprising fitting a plurality of voltage samples to amodel, the plurality of voltage samples furnished by said sampling. 17.The method of claim 15, further comprising averaging a plurality ofvoltage samples, the plurality of voltage samples furnished by saidsampling.
 18. The method of claim 15, further comprising extrapolatingfrom a plurality of voltage samples, the plurality of voltage samplesfurnished by said sampling.
 19. A method of calibrating a response of aNO_(x) sensor, the method comprising: interrupting a bias voltage to anelectrode of the NO_(x) sensor, a current from the electrode responsiveto an exhaust-stream NO_(x) level absent said interrupting; andadjusting a gain of the NO_(x) sensor based at least partly on anattained voltage of the electrode during said interrupting.
 20. Themethod of claim 19, further comprising adjusting an offset of the NO_(x)sensor based at least partly on the attained voltage of the electrodeduring said interrupting.